Yes. Cofigure each timer's output to activate the START input of the other timer. One timer sets the ON time and the other sets the OFF time. Put each timer in the "one-shot" mode.
you can use 555 timer ic. The connection is the normal astable connection of 555 ic with a logic inverter connected to the output pin (i.e, pin 3). The components by calculation that will give you the desired on and off period are: capacitor = 470uF, R1 = 15.4K and R2 = 910k. R1 is connected between pin 6 & 7 and R2 between pin 7 & Vcc. Of course the capacitor is connected between pin 6 & ground.